Minimizing the Transient Response of First-Order Allpass Interpolation

In addition to approaching a pole-zero cancellation at , another undesirable artifact appears as : The transient response also becomes long when the pole at gets close to the unit circle.

A plot of the impulse response for is shown in Fig.3.7. We see a lot of ``ringing'' near half the sampling rate. We actually should expect this from the nonlinear phase distortion which is clearly evident near half the sampling rate in Fig.3.5. We can interpret this phenomenon as the signal components near half the sampling rate being delayed by different amounts than other frequencies, therefore ``sliding out of alignment'' with them.

Figure 3.7: Impulse response of the first-order allpass interpolator for .

For